Christopher Menzel wrote:
> On Jan 21, 2011, at 9:46 AM, doug foxvog wrote:
>
>> ...
>> A standard distinction between a set and a class, is that membership in
>> a [set] cannot change, while membership in a class can.
>>
>
> I think it's useful to distinguish two claims when it comes to the identity
>conditions of classes:
>
> (1) Classes are not extensional (i.e., distinct classes can have the same
>members/instances)
>
> (2) Classes can change their membership.
>
> In the formal semantics of a number of KR languages, (1) is true but,
>strictly speaking at least, (2) is not. Notably, classes in OWL are
>explicitly non-extensional: since a class is stipulated only to *have* an
>extension in OWL's formal semantics, nothing prevents distinct classes from
>having the same extension. The same is true of RDF. However, simply because
>there is no formal notion of change built into OWL's semantics, there is no
>possibility, within a given interpretation, that a class change its
>membership. As noted in an earlier message in this thread, without augmenting
>the notion of an OWL interpretation somehow, change can only be represented
>formally in terms of something like a series of interpretations that are
>thought of as temporally ordered. That said, (2) does seem to be a strong
>*intuitive* idea in the KR, AI, and database communities.
> (01)
The particular problem I have recently got involved in is the intrusion
of temporal concepts into would-be ontologies in business applications.
In the supply-chain area, for example, it is important to be able to
talk about schedules and shipments being "late". Getting past the
indexical issues, which are fixed by translating the intuitive "now"
into specific time relationships, the particular problem is that
shipments and orders do change state, and actions are taken on the basis
of reclassification. (02)
A major problem for us is that the industry folk throw these concepts
into what was an ontology for the "snapshot" model of decision-making --
the state of the world at the time the decision is to be made. This
gives rise to formalizing ideas like "proposition X is false at time A
and true at time B." And that problem arises from the idea that states
of things are characterized by propositions, which seems to be
fundamental to applications of ontologies. The 4D idea that a thing in
a different state is a different thing, and 'objects' are actually
sequences (or more generally, lattices) of things in states, is a means
of producing a formal semantics, but it is totally out of line with the
intuition of the domain experts. They cannot then "validate" the
ontology -- they don't understand it. (03)
I have said in that forum that solving the problem is beyond my
expertise. It is my conviction that the problem is not really "time",
but rather "change of state" or "alternative states", and in that sense,
"time" is a means of labeling "alternative possible worlds". (04)
All we are saying is that the intuitive notion of change is endemic to a
lot of ontology applications. We can usually constrain the immediate
application to avoid the problem or create a convenient work-around, but
that usually means that the next application the business wants to use
the ontology for requires re-writing it. (05)
-Ed (06)
"Mathematicians are like Frenchmen. Whatever you say to them they
translate into their own language and at once it becomes something
entirely different."
-- Goethe (07)
> Finally, the idea that sets are extensional and classes are not is definitely
>not standard among logicians and mathematicians, who typically associate the
>notion of class with theories like VNBG, wherein both classes and sets are
>extensional.
>
> -chris
>
> (08)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800 (09)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (010)
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